Mixed Breeds

i would say yes and yes.

they will tend to take on the qualities of one or the other of the parent's breeds. or a combination of the two breeds' qualities. of course you have to know what the breeds of the parents are. if the parents are mixed breeds, who knows what qualities of the offspring will be.

but what if you mix two similar breeds? say for example, some of the toy breeds.
or some of the working breeds for that matter. there are different types of pointers, english, gordon, short haired, wire haird..
and then you have the sight hounds.... irish and scottish wolf and deer hound.
i'm talking personality though, not looks.
of course breeding dogs with similar looks .. same thing i wonder if it applies... like st bernards and newfoundlands.. though i think they have already crossed the two.. i believe they're called Landseers, but dont quote me on it. i'm not really sure....
.... ok now i'm gonna go look up the history of the landseer.... which i think was created JUST because of Sir Edwin Landseer, the painter.... ha... aint that funny.

Genes do not equalize. A tall Giant breed bred to a small will not produce "middle size dogs"....because both breeds lack the genetics for it. The same with many traits. Genes don't really "dilute to a median" in one breeding. Breeding down or up in size is done over time...unless you have a genetic fluke like dwarfism which can make it stick quite quickly.
 
Breeding a long haired dog to a smooth slick tight coated one will not produce medium coated dogs...and if it does you'd know both sides carry medium coat length. etc etc...
 
One can see in say, the Puggle...what is dominant and recessive in those breeds. Self color...dropped ears....undershot mouths....straight tails...potruding eyes attributes commonly seen. in one or the other breed. And of those things....undershot mouths, straight tails, self color etc....one can also see common traits that have been either selected FOR or AGAINST in the breeds in their development. Beagles can be undershot...it happens...mix that with a Pug that is BRED to be undershot and it exresses some to extremely....Beagle can be self colored because like many scenthounds, tricolor without a ton of  white, used to be a color found in the breed, but it has been largely selected AGAINST...Pugs have a nice tightly curled tail...like Akitas...but I bet like Akitas...sometimes a tail doesn't curl as tight or barely even at all? Fault of course....but common and encouraged in the Beagle, and some Beagles have a tail that touches the back or has a real cuuuurve/ring...that's a fault too, but it happens. Large dark eyes are common to BOTH breeds tho the set in the face is vastly different. But bug eyes do happen in Beagles...again...a fault...but the genetics are still there....link up with the Pug's and there ya go!
 
It seems unique....but aside from a true genetic mutation...there's nothing really unique in the pups...it's all things that the parents carried and expressed or didn't. the uniqueness of the mixed breed dog with unknown/unplanned ancestry comes just from not knowing the pedigree...if you did...a lot of what seems unique would likely be explained.
 
 
ETA: This post ws in response to the OP's post not DumDog's....so ignore the "reply to"...[]

that was actually interesting though, even if it wasnt addressed to me []

so i looked up puggles on dog breed info's website.. talk about some odd ball inconsistent dogs.. one of them is even brindle! where did THAT come from??
i mean i can understand the self coloured and the two tones and the tri-colours.. but brindle? me thinks someone may have not told all the truth when they  bred that dog....
but...  i dunno... do  pugs randomly pop up in brindle  patterns? that new to me...

but as for some other breeds, i know history and genetics play a huge part in it, but... scottish terriers and west highland whites...
well the look similar, and i think... memory is faulty, but isnt there a white scottish terrier? maybe i should say skye terrier, but they all three come from Scotland, so there must be some relations in there, but they branched off for what ever reasons. but they're still terriers and do terrier things...
ok i think i am rambling and its kinda pointless anyway.

still interesting stuff there.